Definition:Statement Form

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Definition

A statement form is a symbolic representation of a compound statement.

It consists of statement variables along with logical connectives joining them.


It is traditional, particularly in the field of mathematical logic, to use lowercase Greek letters to stand for general formulas (the usual ones being $\phi, \psi$ and $\chi$), but more modern treatments are starting to use ordinary lowercase letters of the English alphabet, usually $p, q, r$ etc.


Specific Form

The specific form of a given statement is that propositional formula from which the statement form results from replacing each distinct statement variable by a different simple statement.


Also known as

There are various names for this concept, for example:

  • statement scheme or schema
  • symbolic sentence
  • logical form.

When discussing propositional logic, the terms logical formula or propositional formula are also used.


Examples

Napoleon

Napoleon is dead and the world is rejoicing

has the statement form

$A \land B$

where:

$A$ stands for Napoleon is dead
$B$ stands for The world is rejoicing


Shape of Eggs

If all eggs are not square then all eggs are round

has the statement form

$A \implies B$

where:

$A$ stands for All eggs are not square
$B$ stands for All eggs are round


Barometer

If the barometer falls then either it will rain or it will snow

has the statement form

$A \implies \paren {B \lor C}$

where:

$A$ stands for The barometer falls
$B$ stands for It will rain
$C$ stands for It will snow


Also see


Sources